Question

Sum of 1 to n natural numebrs is 36 find the value of n.​

Answer 1

$\huge\tt\bold\orange{ANSWER}$

$a \: = \: 1 \\ d \: = \: 1 \\ sn \: = \: 36 \\ \frac{n}{2} (2a + (n - 1)d) = 36 \\ \\ \frac{n}{2} (2 + (n - 1)) = 36 \\ \\ n(2 + (n - 1)) = 72 \\ \\ n(n + 1) = 72 \\ \\ {n}^{2} + n - 72 = 0 \\ \\ {n}^{2} + 9n - 8n - 72 = 0 \\ \\ (n - 8)(n + 9) = 0 \\ \\ n \: is \: not \: equal \: to \: 9 \\ n = 8$

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